In this grab taken from video, Britain’s Prime Minister Theresa May speaks during Prime Minister’s Questions in the House of Commons, London, Wednesday March 27, 2019. British lawmakers are preparing to vote Wednesday on alternatives for leaving the European Union as they seek to end an impasse following the overwhelming defeat of the deal negotiated by Prime Minister Theresa May.

LONDON — British Prime Minister Theresa May offered up her job in exchange for her Brexit deal Wednesday, telling colleagues she would quit within weeks if the agreement was passed and Britain left the European Union.

May’s dramatic concession that “there is a desire for a new approach – and new leadership” was a last-ditch effort to bring enough reluctant colleagues on board to push her twice-rejected EU divorce deal over the line.

It looked like it might not be enough, as a key Northern Ireland party said it would not be supporting the deal.

May’s announcement came as lawmakers held an inconclusive series of votes on alternatives to her unpopular deal. It was the first step in an attempt by Parliament to break the Brexit deadlock and stop the country from tumbling out of the bloc within weeks with no exit plan in place.

May has been under mounting pressure from pro-Brexit members of her Conservative Party to quit. Many Brexiteers accuse her of negotiating a bad divorce deal that leaves Britain too closely tied to the bloc after it leaves.

Several have said they would support the withdrawal deal if another leader took charge of the next stage of negotiations, which will determine Britain’s future relations with the EU.

In a packed meeting of Conservative legislators described by participants as “somber,” May finally conceded she would have to go, although she did not set a departure date.

“I am prepared to leave this job earlier than I intended in order to do what is right for our country and our party,” she said, according to a transcript released by her office.

Anti-EU lawmaker Jacob Rees-Mogg, who has clashed with May throughout the Brexit process, said she had been “very clear” that if Britain leaves the EU as foreseen on May 22, she will quit soon after.

He said the prime minister had been “very dignified.”

“She put her case well, and reiterated that she had done her duty,” he said.

It was unclear whether May’s offer to resign would be enough to win backing for her deal, which was defeated by 230 votes in January and by 149 votes earlier this month.

High-profile Brexiteer Boris Johnson announced soon after May’s statement that he would support the agreement, which he has previously called a “humiliation.” Johnson is a likely contender to replace May as prime minister.

But other hard-liners said they would continue to reject the deal, and Northern Ireland’s small but influential Democratic Unionist Party refused to budge in its opposition to the deal.

The DUP’s support was seen as key to persuading other Brexiteers to back the deal. But the staunchly pro-British party fears a provision designed keep an open border between EU member Ireland and the U.K.’s Northern Ireland after Brexit would weaken the bonds between Northern Ireland and the rest of the U.K.

Asked if the party might abstain instead, DUP lawmaker Nigel Dodds tweeted: “The DUP do not abstain on the Union.”

Two years ago, Britain triggered a countdown to departure from the EU that ended Friday, March 29, 2019. With that date approaching and no Brexit deal approved by Britain, the EU last week granted a delay. It said that if Parliament approves the proposed divorce deal this week, the U.K. will leave the EU on May 22. If not, the government has until April 12 to tell the 27 remaining EU countries what it plans to do: leave without a deal, cancel Brexit or propose a radically new path.

With May clinging to her Plan A — getting her deal approved — lawmakers this week seized control of the parliamentary timetable for debate and votes Wednesday on a range of Brexit alternatives.

The results underscored the divisions in Parliament, and the country, over Brexit. None of the eight plans received a majority of votes. The most popular were a proposal to remain in a customs union with the bloc, which was defeated 272-264, and a call to hold a public referendum on any divorce deal, which fell by 295 votes to 268. Both ideas got more support than the 242 votes secured by May’s deal earlier this month.

A call to leave the EU without a deal was supported by 160 lawmakers and opposed by 400.

The plan is for the most popular ideas to move to a second vote Monday to find an option that can command a majority. Parliament would then instruct the government to negotiate it with the EU.

May has said she will consider the outcome of the votes, although she has refused to be bound by the result.

Brexit Secretary Stephen Barclay urged lawmakers to back May’s deal, saying the ambiguous result “demonstrates that there are no easy options here.”

Barclay said he had introduced a motion to have Parliament meet Friday if needed for a vote on May’s agreement, but it remained unclear whether it would go ahead. House of Commons Speaker John Bercow said he would not accept another vote on the twice-rejected deal unless substantial changes were made.

Wednesday’s votes produced inconclusive results, but could push Britain in the direction of a softer Brexit that keeps Britain closely tied economically to the EU.

That would probably require the U.K. to seek a longer delay, although that would mean participating in May 23-26 European Parliament elections.

Many EU officials are keen to avoid the messy participation of a departing member state.

But the chief of the European Council told European lawmakers that the EU should let Britain take part if the country indicated it planned to change course on Brexit. Donald Tusk said the bloc could not “betray” the millions of Britons who want to stay in the EU.

“They may feel they are not sufficiently represented by the U.K. Parliament but they must feel that they are represented by you in this chamber. Because they are Europeans,” Tusk said.

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Gregory Katz and Tobie Mathew in London and Raf Casert in Strasbourg, France, contributed.

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LONDON — Theresa May announced Friday that she will step down as U.K. Conservative Party leader on June 7, admitting defeat in her attempt to take Britain out of the European Union and sparking a contest to become the country’s next prime minister. She will stay as caretaker prime minister until the new leader is chosen, a process likely to...